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Cited by 455

The DOI matches its Crossref record; 23 of the 23 references it cites were found in a registry or an index.

On the Estimation of Confidence Intervals for Binomial Population Proportions in Astronomy: The Simplicity and Superiority of the Bayesian Approach

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Cameron, Ewan·2011·Publications of the Astronomical Society of Australia
DOI 10.1071/as10046
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Abstract

I present a critical review of techniques for estimating confidence intervals on binomial population proportions inferred from success counts in small to intermediate samples. Population proportions arise frequently as quantities of interest in astronomical research; for instance, in studies aiming to constrain the bar fraction, active galactic nucleus fraction, supermassive black hole fraction, merger fraction, or red sequence fraction from counts of galaxies exhibiting distinct morphological features or stellar populations. However, two of the most widely-used techniques for estimating binomial confidence intervals — the ‘normal approximation’ and the Clopper & Pearson approach — are liable to misrepresent the degree of statistical uncertainty present under sampling conditions routinely encountered in astronomical surveys, leading to an ineffective use of the experimental data (and, worse, an inefficient use of the resources expended in obtaining that data). Hence, I provide here an overview of the fundamentals of binomial statistics with two principal aims: (I) to reveal the ease with which (Bayesian) binomial confidence intervals with more satisfactory behaviour may be estimated from the quantiles of the beta distribution using modern mathematical software packages (e.g.r, matlab, mathematica, idl, python); and (ii) to demonstrate convincingly the major flaws of both the ‘normal approximation’ and the Clopper & Pearson approach for error estimation.

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Research works printed but not linked: 5

  1. 10.1086/169424 · doi:10.1086/169424
  2. 10.1111/j.1365-2966.2010.17314.x · doi:10.1111/j.1365-2966.2010.17314.x
  3. Quirin, 1978, Probability and Statistics
  4. López-Sanjuan, 2010, AandA, 518, 20
  5. 10.1086/341647 · doi:10.1086/341647

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Metadata

Authors
Cameron, E.
Venue
Publications of the Astronomical Society of Australia
Publisher
Cambridge University Press (CUP)
Published
2011
Volume
28
Issue
2
Pages
128-139
ISSN
  • 1323-3580 (ISSN-L)
  • 1448-6083
DOI
10.1071/as10046
OpenAlex
W2131462587
Cited by
455
References
23
FWCI
26.71
Type
journal article
Language
en
Open access
bronze
Licence
www.cambridge.org/core/terms (unspecified, 732 d)

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CoChat. (2026). Citation check: On the Estimation of Confidence Intervals for Binomial Population Proportions in Astronomy: The Simplicity and Superiority of the Bayesian Approach. https://app.cochat.ai/papers/10.1071/as10046
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Cameron, E. (2011). On the Estimation of Confidence Intervals for Binomial Population Proportions in Astronomy: The Simplicity and Superiority of the Bayesian Approach. Publications of the Astronomical Society of Australia. https://doi.org/10.1071/as10046

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